Find the Exact Value cot(330)

Problem

cot(330^∘)

Solution

1. Identify the reference angle by finding the difference between 330^∘ and 360^∘

(θ_ref)=360^∘−330^∘=30^∘

2. Determine the quadrant of the angle 330^∘ which is in Quadrant IV.

Quadrant IV

3. Determine the sign of the cotangent function in Quadrant IV, where tangent and cotangent are negative.

cot(330^∘)=−cot(30^∘)

4. Apply the known exact value for cot(30^∘) which is √(,3)

cot(30^∘)=√(,3)

5. Combine the sign and the value to find the final result.

cot(330^∘)=−√(,3)

Final Answer

cot(330^∘)=−√(,3)

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